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org.apache.commons.math3.complex</FONT>
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Class Complex</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.complex.Complex</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A>, <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>Complex</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;, <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DL>
</PRE>

<P>
Representation of a Complex number, i.e. a number which has both a
 real and imaginary part.
 <br/>
 Implementations of arithmetic operations handle <code>NaN</code> and
 infinite values according to the rules for <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><CODE>Double</CODE></A>, i.e.
 <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#equals(java.lang.Object)"><CODE>equals(java.lang.Object)</CODE></A> is an equivalence relation for all instances that have
 a <code>NaN</code> in either real or imaginary part, e.g. the following are
 considered equal:
 <ul>
  <li><code>1 + NaNi</code></li>
  <li><code>NaN + i</code></li>
  <li><code>NaN + NaNi</code></li>
 </ul>
 Note that this is in contradiction with the IEEE-754 standard for floating
 point numbers (according to which the test <code>x == x</code> must fail if
 <code>x</code> is <code>NaN</code>). The method
 <A HREF="../../../../../org/apache/commons/math3/util/Precision.html#equals(double, double, int)"><CODE>equals for primitive double</CODE></A> in <A HREF="../../../../../org/apache/commons/math3/util/Precision.html" title="class in org.apache.commons.math3.util"><CODE>Precision</CODE></A>
 conforms with IEEE-754 while this class conforms with the standard behavior
 for Java object types.
 <br/>
 Implements Serializable since 2.0
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: Complex.java 1459927 2013-03-22 18:55:58Z luc $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../serialized-form.html#org.apache.commons.math3.complex.Complex">Serialized Form</A></DL>
<HR>

<P>
<!-- =========== FIELD SUMMARY =========== -->

<A NAME="field_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Field Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#I">I</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The square root of -1.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#INF">INF</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A complex number representing "+INF + INFi"</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN">NaN</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A complex number representing "NaN + NaNi"</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#ONE">ONE</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A complex number representing "1.0 + 0.0i"</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#ZERO">ZERO</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A complex number representing "0.0 + 0.0i"</TD>
</TR>
</TABLE>
&nbsp;
<!-- ======== CONSTRUCTOR SUMMARY ======== -->

<A NAME="constructor_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Constructor Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#Complex(double)">Complex</A></B>(double&nbsp;real)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a complex number given only the real part.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#Complex(double, double)">Complex</A></B>(double&nbsp;real,
        double&nbsp;imaginary)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a complex number given the real and imaginary parts.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#abs()">abs</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the absolute value of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#acos()">acos</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top">
 inverse cosine</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#add(org.apache.commons.math3.complex.Complex)">add</A></B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;addend)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is
 <code>(this + addend)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#add(double)">add</A></B>(double&nbsp;addend)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>(this + addend)</code>,
 with <code>addend</code> interpreted as a real number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#asin()">asin</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top">
 inverse sine</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#atan()">atan</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top">
 inverse tangent</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#conjugate()">conjugate</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the conjugate of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#cos()">cos</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top">
 cosine</a>
 of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#cosh()">cosh</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top">
 hyperbolic cosine</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#createComplex(double, double)">createComplex</A></B>(double&nbsp;realPart,
              double&nbsp;imaginaryPart)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a complex number given the real and imaginary parts.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#divide(org.apache.commons.math3.complex.Complex)">divide</A></B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;divisor)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is
 <code>(this / divisor)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#divide(double)">divide</A></B>(double&nbsp;divisor)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>(this / divisor)</code>,
 with <code>divisor</code> interpreted as a real number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#equals(java.lang.Object)">equals</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;other)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Test for the equality of two Complex objects.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#exp()">exp</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top">
 exponential function</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#getArgument()">getArgument</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the argument of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/ComplexField.html" title="class in org.apache.commons.math3.complex">ComplexField</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#getField()">getField</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the <A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3"><CODE>Field</CODE></A> to which the instance belongs.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#getImaginary()">getImaginary</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the imaginary part.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#getReal()">getReal</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the real part.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#hashCode()">hashCode</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get a hashCode for the complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#isInfinite()">isInfinite</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Checks whether either the real or imaginary part of this complex number
 takes an infinite value (either <code>Double.POSITIVE_INFINITY</code> or
 <code>Double.NEGATIVE_INFINITY</code>) and neither part
 is <code>NaN</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#isNaN()">isNaN</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Checks whether either or both parts of this complex number is
 <code>NaN</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#log()">log</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top">
 natural logarithm</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#multiply(org.apache.commons.math3.complex.Complex)">multiply</A></B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;factor)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>this * factor</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#multiply(double)">multiply</A></B>(double&nbsp;factor)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>this * factor</code>, with <code>factor</code>
 interpreted as a real number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#multiply(int)">multiply</A></B>(int&nbsp;factor)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>this * factor</code>, with <code>factor</code>
 interpreted as a integer number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#negate()">negate</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is <code>(-this)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#nthRoot(int)">nthRoot</A></B>(int&nbsp;n)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the n-th roots of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#pow(org.apache.commons.math3.complex.Complex)">pow</A></B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns of value of this complex number raised to the power of <code>x</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#pow(double)">pow</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns of value of this complex number raised to the power of <code>x</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#readResolve()">readResolve</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Resolve the transient fields in a deserialized Complex Object.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#reciprocal()">reciprocal</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the multiplicative inverse of <code>this</code> element.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#sin()">sin</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
 sine</a>
 of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#sinh()">sinh</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
 hyperbolic sine</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#sqrt()">sqrt</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
 square root</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#sqrt1z()">sqrt1z</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
 square root</a> of <code>1 - this<sup>2</sup></code> for this complex
 number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#subtract(org.apache.commons.math3.complex.Complex)">subtract</A></B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;subtrahend)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is
 <code>(this - subtrahend)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#subtract(double)">subtract</A></B>(double&nbsp;subtrahend)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <code>Complex</code> whose value is
 <code>(this - subtrahend)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#tan()">tan</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top">
 tangent</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#tanh()">tanh</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
 hyperbolic tangent</a> of this complex number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#toString()">toString</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#valueOf(double)">valueOf</A></B>(double&nbsp;realPart)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a complex number given only the real part.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#valueOf(double, double)">valueOf</A></B>(double&nbsp;realPart,
        double&nbsp;imaginaryPart)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Create a complex number given the real and imaginary parts.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ============ FIELD DETAIL =========== -->

<A NAME="field_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Field Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="I"><!-- --></A><H3>
I</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>I</B></PRE>
<DL>
<DD>The square root of -1. A number representing "0.0 + 1.0i"
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="NaN"><!-- --></A><H3>
NaN</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>NaN</B></PRE>
<DL>
<DD>A complex number representing "NaN + NaNi"
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="INF"><!-- --></A><H3>
INF</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>INF</B></PRE>
<DL>
<DD>A complex number representing "+INF + INFi"
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="ONE"><!-- --></A><H3>
ONE</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>ONE</B></PRE>
<DL>
<DD>A complex number representing "1.0 + 0.0i"
<P>
<DL>
</DL>
</DL>
<HR>

<A NAME="ZERO"><!-- --></A><H3>
ZERO</H3>
<PRE>
public static final <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>ZERO</B></PRE>
<DL>
<DD>A complex number representing "0.0 + 0.0i"
<P>
<DL>
</DL>
</DL>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Constructor Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="Complex(double)"><!-- --></A><H3>
Complex</H3>
<PRE>
public <B>Complex</B>(double&nbsp;real)</PRE>
<DL>
<DD>Create a complex number given only the real part.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>real</CODE> - Real part.</DL>
</DL>
<HR>

<A NAME="Complex(double, double)"><!-- --></A><H3>
Complex</H3>
<PRE>
public <B>Complex</B>(double&nbsp;real,
               double&nbsp;imaginary)</PRE>
<DL>
<DD>Create a complex number given the real and imaginary parts.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>real</CODE> - Real part.<DD><CODE>imaginary</CODE> - Imaginary part.</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="abs()"><!-- --></A><H3>
abs</H3>
<PRE>
public double <B>abs</B>()</PRE>
<DL>
<DD>Return the absolute value of this complex number.
 Returns <code>NaN</code> if either real or imaginary part is <code>NaN</code>
 and <code>Double.POSITIVE_INFINITY</code> if neither part is <code>NaN</code>,
 but at least one part is infinite.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the absolute value.</DL>
</DD>
</DL>
<HR>

<A NAME="add(org.apache.commons.math3.complex.Complex)"><!-- --></A><H3>
add</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>add</B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;addend)
            throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is
 <code>(this + addend)</code>.
 Uses the definitional formula
 <pre>
  <code>
   (a + bi) + (c + di) = (a+c) + (b+d)i
  </code>
 </pre>
 <br/>
 If either <code>this</code> or <code>addend</code> has a <code>NaN</code> value in
 either part, <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned; otherwise <code>Infinite</code>
 and <code>NaN</code> values are returned in the parts of the result
 according to the rules for <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><CODE>Double</CODE></A> arithmetic.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#add(T)">add</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>addend</CODE> - Value to be added to this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this + addend</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>addend</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="add(double)"><!-- --></A><H3>
add</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>add</B>(double&nbsp;addend)</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>(this + addend)</code>,
 with <code>addend</code> interpreted as a real number.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>addend</CODE> - Value to be added to this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this + addend</code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#add(org.apache.commons.math3.complex.Complex)"><CODE>add(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="conjugate()"><!-- --></A><H3>
conjugate</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>conjugate</B>()</PRE>
<DL>
<DD>Return the conjugate of this complex number.
 The conjugate of <code>a + bi</code> is <code>a - bi</code>.
 <br/>
 <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned if either the real or imaginary
 part of this Complex number equals <code>Double.NaN</code>.
 <br/>
 If the imaginary part is infinite, and the real part is not
 <code>NaN</code>, the returned value has infinite imaginary part
 of the opposite sign, e.g. the conjugate of
 <code>1 + POSITIVE_INFINITY i</code> is <code>1 - NEGATIVE_INFINITY i</code>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the conjugate of this Complex object.</DL>
</DD>
</DL>
<HR>

<A NAME="divide(org.apache.commons.math3.complex.Complex)"><!-- --></A><H3>
divide</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>divide</B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;divisor)
               throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is
 <code>(this / divisor)</code>.
 Implements the definitional formula
 <pre>
  <code>
    a + bi          ac + bd + (bc - ad)i
    ----------- = -------------------------
    c + di         c<sup>2</sup> + d<sup>2</sup>
  </code>
 </pre>
 but uses
 <a href="http://doi.acm.org/10.1145/1039813.1039814">
 prescaling of operands</a> to limit the effects of overflows and
 underflows in the computation.
 <br/>
 <code>Infinite</code> and <code>NaN</code> values are handled according to the
 following rules, applied in the order presented:
 <ul>
  <li>If either <code>this</code> or <code>divisor</code> has a <code>NaN</code> value
   in either part, <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned.
  </li>
  <li>If <code>divisor</code> equals <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#ZERO"><CODE>ZERO</CODE></A>, <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned.
  </li>
  <li>If <code>this</code> and <code>divisor</code> are both infinite,
   <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned.
  </li>
  <li>If <code>this</code> is finite (i.e., has no <code>Infinite</code> or
   <code>NaN</code> parts) and <code>divisor</code> is infinite (one or both parts
   infinite), <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#ZERO"><CODE>ZERO</CODE></A> is returned.
  </li>
  <li>If <code>this</code> is infinite and <code>divisor</code> is finite,
   <code>NaN</code> values are returned in the parts of the result if the
   <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><CODE>Double</CODE></A> rules applied to the definitional formula
   force <code>NaN</code> results.
  </li>
 </ul>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#divide(T)">divide</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>divisor</CODE> - Value by which this <code>Complex</code> is to be divided.
<DT><B>Returns:</B><DD><code>this / divisor</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>divisor</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="divide(double)"><!-- --></A><H3>
divide</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>divide</B>(double&nbsp;divisor)</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>(this / divisor)</code>,
 with <code>divisor</code> interpreted as a real number.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>divisor</CODE> - Value by which this <code>Complex</code> is to be divided.
<DT><B>Returns:</B><DD><code>this / divisor</code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#divide(org.apache.commons.math3.complex.Complex)"><CODE>divide(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="reciprocal()"><!-- --></A><H3>
reciprocal</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>reciprocal</B>()</PRE>
<DL>
<DD>Returns the multiplicative inverse of <code>this</code> element.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#reciprocal()">reciprocal</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the inverse of <code>this</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="equals(java.lang.Object)"><!-- --></A><H3>
equals</H3>
<PRE>
public boolean <B>equals</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A>&nbsp;other)</PRE>
<DL>
<DD>Test for the equality of two Complex objects.
 If both the real and imaginary parts of two complex numbers
 are exactly the same, and neither is <code>Double.NaN</code>, the two
 Complex objects are considered to be equal.
 All <code>NaN</code> values are considered to be equal - i.e, if either
 (or both) real and imaginary parts of the complex number are equal
 to <code>Double.NaN</code>, the complex number is equal to
 <code>NaN</code>.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A></CODE> in class <CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>other</CODE> - Object to test for equality to this
<DT><B>Returns:</B><DD>true if two Complex objects are equal, false if object is
 <code>null</code>, not an instance of Complex, or not equal to this Complex
 instance.</DL>
</DD>
</DL>
<HR>

<A NAME="hashCode()"><!-- --></A><H3>
hashCode</H3>
<PRE>
public int <B>hashCode</B>()</PRE>
<DL>
<DD>Get a hashCode for the complex number.
 Any <code>Double.NaN</code> value in real or imaginary part produces
 the same hash code <code>7</code>.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A></CODE> in class <CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>a hash code value for this object.</DL>
</DD>
</DL>
<HR>

<A NAME="getImaginary()"><!-- --></A><H3>
getImaginary</H3>
<PRE>
public double <B>getImaginary</B>()</PRE>
<DL>
<DD>Access the imaginary part.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the imaginary part.</DL>
</DD>
</DL>
<HR>

<A NAME="getReal()"><!-- --></A><H3>
getReal</H3>
<PRE>
public double <B>getReal</B>()</PRE>
<DL>
<DD>Access the real part.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the real part.</DL>
</DD>
</DL>
<HR>

<A NAME="isNaN()"><!-- --></A><H3>
isNaN</H3>
<PRE>
public boolean <B>isNaN</B>()</PRE>
<DL>
<DD>Checks whether either or both parts of this complex number is
 <code>NaN</code>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>true if either or both parts of this complex number is
 <code>NaN</code>; false otherwise.</DL>
</DD>
</DL>
<HR>

<A NAME="isInfinite()"><!-- --></A><H3>
isInfinite</H3>
<PRE>
public boolean <B>isInfinite</B>()</PRE>
<DL>
<DD>Checks whether either the real or imaginary part of this complex number
 takes an infinite value (either <code>Double.POSITIVE_INFINITY</code> or
 <code>Double.NEGATIVE_INFINITY</code>) and neither part
 is <code>NaN</code>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>true if one or both parts of this complex number are infinite
 and neither part is <code>NaN</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="multiply(org.apache.commons.math3.complex.Complex)"><!-- --></A><H3>
multiply</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>multiply</B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;factor)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>this * factor</code>.
 Implements preliminary checks for <code>NaN</code> and infinity followed by
 the definitional formula:
 <pre>
  <code>
   (a + bi)(c + di) = (ac - bd) + (ad + bc)i
  </code>
 </pre>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either <code>this</code> or <code>factor</code> has one or
 more <code>NaN</code> parts.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#INF"><CODE>INF</CODE></A> if neither <code>this</code> nor <code>factor</code> has one
 or more <code>NaN</code> parts and if either <code>this</code> or <code>factor</code>
 has one or more infinite parts (same result is returned regardless of
 the sign of the components).
 <br/>
 Returns finite values in components of the result per the definitional
 formula in all remaining cases.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#multiply(T)">multiply</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>factor</CODE> - value to be multiplied by this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this * factor</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>factor</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="multiply(int)"><!-- --></A><H3>
multiply</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>multiply</B>(int&nbsp;factor)</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>this * factor</code>, with <code>factor</code>
 interpreted as a integer number.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#multiply(int)">multiply</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>factor</CODE> - value to be multiplied by this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this * factor</code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#multiply(org.apache.commons.math3.complex.Complex)"><CODE>multiply(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="multiply(double)"><!-- --></A><H3>
multiply</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>multiply</B>(double&nbsp;factor)</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>this * factor</code>, with <code>factor</code>
 interpreted as a real number.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>factor</CODE> - value to be multiplied by this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this * factor</code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#multiply(org.apache.commons.math3.complex.Complex)"><CODE>multiply(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="negate()"><!-- --></A><H3>
negate</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>negate</B>()</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is <code>(-this)</code>.
 Returns <code>NaN</code> if either real or imaginary
 part of this Complex number equals <code>Double.NaN</code>.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#negate()">negate</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD><code>-this</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="subtract(org.apache.commons.math3.complex.Complex)"><!-- --></A><H3>
subtract</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>subtract</B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;subtrahend)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is
 <code>(this - subtrahend)</code>.
 Uses the definitional formula
 <pre>
  <code>
   (a + bi) - (c + di) = (a-c) + (b-d)i
  </code>
 </pre>
 If either <code>this</code> or <code>subtrahend</code> has a <code>NaN]</code> value in either part,
 <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned; otherwise infinite and <code>NaN</code> values are
 returned in the parts of the result according to the rules for
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><CODE>Double</CODE></A> arithmetic.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#subtract(T)">subtract</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>subtrahend</CODE> - value to be subtracted from this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this - subtrahend</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if <code>subtrahend</code> is <code>null</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="subtract(double)"><!-- --></A><H3>
subtract</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>subtract</B>(double&nbsp;subtrahend)</PRE>
<DL>
<DD>Returns a <code>Complex</code> whose value is
 <code>(this - subtrahend)</code>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>subtrahend</CODE> - value to be subtracted from this <code>Complex</code>.
<DT><B>Returns:</B><DD><code>this - subtrahend</code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#subtract(org.apache.commons.math3.complex.Complex)"><CODE>subtract(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="acos()"><!-- --></A><H3>
acos</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>acos</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top">
 inverse cosine</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))
  </code>
 </pre>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code> or infinite.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the inverse cosine of this complex number.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="asin()"><!-- --></A><H3>
asin</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>asin</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top">
 inverse sine</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))
  </code>
 </pre>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code> or infinite.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the inverse sine of this complex number.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="atan()"><!-- --></A><H3>
atan</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>atan</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top">
 inverse tangent</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   atan(z) = (i/2) log((i + z)/(i - z))
  </code>
 </pre>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code> or infinite.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the inverse tangent of this complex number<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="cos()"><!-- --></A><H3>
cos</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>cos</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top">
 cosine</a>
 of this complex number.
 Implements the formula:
 <pre>
  <code>
   cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sin(double)" title="class or interface in java.lang"><CODE>Math.sin(double)</CODE></A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#cos(double)" title="class or interface in java.lang"><CODE>Math.cos(double)</CODE></A>,
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   cos(1 &plusmn; INFINITY i) = 1 &#x2213; INFINITY i
   cos(&plusmn;INFINITY + i) = NaN + NaN i
   cos(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the cosine of this complex number.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="cosh()"><!-- --></A><H3>
cosh</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>cosh</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top">
 hyperbolic cosine</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i}
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sin(double)" title="class or interface in java.lang"><CODE>Math.sin(double)</CODE></A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#cos(double)" title="class or interface in java.lang"><CODE>Math.cos(double)</CODE></A>,
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   cosh(1 &plusmn; INFINITY i) = NaN + NaN i
   cosh(&plusmn;INFINITY + i) = INFINITY &plusmn; INFINITY i
   cosh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the hyperbolic cosine of this complex number.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="exp()"><!-- --></A><H3>
exp</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>exp</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top">
 exponential function</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#exp(double)" title="class or interface in java.lang"><CODE>Math.exp(double)</CODE></A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#cos(double)" title="class or interface in java.lang"><CODE>Math.cos(double)</CODE></A>, and
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sin(double)" title="class or interface in java.lang"><CODE>Math.sin(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   exp(1 &plusmn; INFINITY i) = NaN + NaN i
   exp(INFINITY + i) = INFINITY + INFINITY i
   exp(-INFINITY + i) = 0 + 0i
   exp(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD><code><i>e</i><sup>this</sup></code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="log()"><!-- --></A><H3>
log</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>log</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top">
 natural logarithm</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   log(a + bi) = ln(|a + bi|) + arg(a + bi)i
  </code>
 </pre>
 where ln on the right hand side is <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#log(double)" title="class or interface in java.lang"><CODE>Math.log(double)</CODE></A>,
 <code>|a + bi|</code> is the modulus, <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#abs()"><CODE>abs()</CODE></A>,  and
 <code>arg(a + bi) = </code><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#atan2(double, double)" title="class or interface in java.lang"><CODE>Math.atan2(double, double)</CODE></A>(b, a).
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite (or critical) values in real or imaginary parts of the input may
 result in infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   log(1 &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/2)i
   log(INFINITY + i) = INFINITY + 0i
   log(-INFINITY + i) = INFINITY + &pi;i
   log(INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/4)i
   log(-INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (3&pi;/4)i
   log(0 + 0i) = -INFINITY + 0i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the value <code>ln &nbsp; this</code>, the natural logarithm
 of <code>this</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="pow(org.apache.commons.math3.complex.Complex)"><!-- --></A><H3>
pow</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>pow</B>(<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&nbsp;x)
            throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Returns of value of this complex number raised to the power of <code>x</code>.
 Implements the formula:
 <pre>
  <code>
   y<sup>x</sup> = exp(x&middot;log(y))
  </code>
 </pre>
 where <code>exp</code> and <code>log</code> are <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#exp()"><CODE>exp()</CODE></A> and
 <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#log()"><CODE>log()</CODE></A>, respectively.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code> or infinite, or if <code>y</code>
 equals <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#ZERO"><CODE>ZERO</CODE></A>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - exponent to which this <code>Complex</code> is to be raised.
<DT><B>Returns:</B><DD><code> this<sup><code>x</code></sup></code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if x is <code>null</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="pow(double)"><!-- --></A><H3>
pow</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>pow</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns of value of this complex number raised to the power of <code>x</code>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - exponent to which this <code>Complex</code> is to be raised.
<DT><B>Returns:</B><DD><code>this<sup>x</sup></code>.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#pow(org.apache.commons.math3.complex.Complex)"><CODE>pow(Complex)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="sin()"><!-- --></A><H3>
sin</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>sin</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
 sine</a>
 of this complex number.
 Implements the formula:
 <pre>
  <code>
   sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sin(double)" title="class or interface in java.lang"><CODE>Math.sin(double)</CODE></A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#cos(double)" title="class or interface in java.lang"><CODE>Math.cos(double)</CODE></A>,
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or <code>NaN</code> values returned in parts of the result.
 <pre>
  Examples:
  <code>
   sin(1 &plusmn; INFINITY i) = 1 &plusmn; INFINITY i
   sin(&plusmn;INFINITY + i) = NaN + NaN i
   sin(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the sine of this complex number.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="sinh()"><!-- --></A><H3>
sinh</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>sinh</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
 hyperbolic sine</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#sin(double)" title="class or interface in java.lang"><CODE>Math.sin(double)</CODE></A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#cos(double)" title="class or interface in java.lang"><CODE>Math.cos(double)</CODE></A>,
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   sinh(1 &plusmn; INFINITY i) = NaN + NaN i
   sinh(&plusmn;INFINITY + i) = &plusmn; INFINITY + INFINITY i
   sinh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the hyperbolic sine of <code>this</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="sqrt()"><!-- --></A><H3>
sqrt</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>sqrt</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
 square root</a> of this complex number.
 Implements the following algorithm to compute <code>sqrt(a + bi)</code>:
 <ol><li>Let <code>t = sqrt((|a| + |a + bi|) / 2)</code></li>
 <li><pre>if <code>a &amp;#8805; 0</code> return <code>t + (b/2t)i</code>
  else return <code>|b|/2t + sign(b)t i </code></pre></li>
 </ol>
 where <ul>
 <li><code>|a| = </code><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Math.html?is-external=true#abs(int)" title="class or interface in java.lang"><CODE>Math.abs(int)</CODE></A>(a)</li>
 <li><code>|a + bi| = </code><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#abs()"><CODE>abs()</CODE></A>(a + bi)</li>
 <li><code>sign(b) =  </code><A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#copySign(double, double)"><CODE>copySign(1d, b)</CODE></A>
 </ul>
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   sqrt(1 &plusmn; INFINITY i) = INFINITY + NaN i
   sqrt(INFINITY + i) = INFINITY + 0i
   sqrt(-INFINITY + i) = 0 + INFINITY i
   sqrt(INFINITY &plusmn; INFINITY i) = INFINITY + NaN i
   sqrt(-INFINITY &plusmn; INFINITY i) = NaN &plusmn; INFINITY i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the square root of <code>this</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="sqrt1z()"><!-- --></A><H3>
sqrt1z</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>sqrt1z</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top">
 square root</a> of <code>1 - this<sup>2</sup></code> for this complex
 number.
 Computes the result directly as
 <code>sqrt(ONE.subtract(z.multiply(z)))</code>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the square root of <code>1 - this<sup>2</sup></code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="tan()"><!-- --></A><H3>
tan</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>tan</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top">
 tangent</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sin(double)"><CODE>FastMath.sin(double)</CODE></A>, <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cos(double)"><CODE>FastMath.cos(double)</CODE></A>, <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite (or critical) values in real or imaginary parts of the input may
 result in infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   tan(a &plusmn; INFINITY i) = 0 &plusmn; i
   tan(&plusmn;INFINITY + bi) = NaN + NaN i
   tan(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
   tan(&plusmn;&pi;/2 + 0 i) = &plusmn;INFINITY + NaN i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the tangent of <code>this</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="tanh()"><!-- --></A><H3>
tanh</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>tanh</B>()</PRE>
<DL>
<DD>Compute the
 <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
 hyperbolic tangent</a> of this complex number.
 Implements the formula:
 <pre>
  <code>
   tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
  </code>
 </pre>
 where the (real) functions on the right-hand side are
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sin(double)"><CODE>FastMath.sin(double)</CODE></A>, <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cos(double)"><CODE>FastMath.cos(double)</CODE></A>, <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#cosh(double)"><CODE>FastMath.cosh(double)</CODE></A> and
 <A HREF="../../../../../org/apache/commons/math3/util/FastMath.html#sinh(double)"><CODE>FastMath.sinh(double)</CODE></A>.
 <br/>
 Returns <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> if either real or imaginary part of the
 input argument is <code>NaN</code>.
 <br/>
 Infinite values in real or imaginary parts of the input may result in
 infinite or NaN values returned in parts of the result.
 <pre>
  Examples:
  <code>
   tanh(a &plusmn; INFINITY i) = NaN + NaN i
   tanh(&plusmn;INFINITY + bi) = &plusmn;1 + 0 i
   tanh(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
   tanh(0 + (&pi;/2)i) = NaN + INFINITY i
  </code>
 </pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the hyperbolic tangent of <code>this</code>.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getArgument()"><!-- --></A><H3>
getArgument</H3>
<PRE>
public double <B>getArgument</B>()</PRE>
<DL>
<DD>Compute the argument of this complex number.
 The argument is the angle phi between the positive real axis and
 the point representing this number in the complex plane.
 The value returned is between -PI (not inclusive)
 and PI (inclusive), with negative values returned for numbers with
 negative imaginary parts.
 <br/>
 If either real or imaginary part (or both) is NaN, NaN is returned.
 Infinite parts are handled as <code>Math.atan2</code> handles them,
 essentially treating finite parts as zero in the presence of an
 infinite coordinate and returning a multiple of pi/4 depending on
 the signs of the infinite parts.
 See the javadoc for <code>Math.atan2</code> for full details.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the argument of <code>this</code>.</DL>
</DD>
</DL>
<HR>

<A NAME="nthRoot(int)"><!-- --></A><H3>
nthRoot</H3>
<PRE>
public <A HREF="http://download.oracle.com/javase/6/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt; <B>nthRoot</B>(int&nbsp;n)
                      throws <A HREF="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</A></PRE>
<DL>
<DD>Computes the n-th roots of this complex number.
 The nth roots are defined by the formula:
 <pre>
  <code>
   z<sub>k</sub> = abs<sup>1/n</sup> (cos(phi + 2&pi;k/n) + i (sin(phi + 2&pi;k/n))
  </code>
 </pre>
 for <i><code>k=0, 1, ..., n-1</code></i>, where <code>abs</code> and <code>phi</code>
 are respectively the <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#abs()"><CODE>modulus</CODE></A> and
 <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#getArgument()"><CODE>argument</CODE></A> of this complex number.
 <br/>
 If one or both parts of this complex number is NaN, a list with just
 one element, <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#NaN"><CODE>NaN</CODE></A> is returned.
 if neither part is NaN, but at least one part is infinite, the result
 is a one-element list containing <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#INF"><CODE>INF</CODE></A>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>n</CODE> - Degree of root.
<DT><B>Returns:</B><DD>a List<Complex> of all <code>n</code>-th roots of <code>this</code>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NotPositiveException.html" title="class in org.apache.commons.math3.exception">NotPositiveException</A></CODE> - if <code>n &lt;= 0</code>.<DT><B>Since:</B></DT>
  <DD>2.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="createComplex(double, double)"><!-- --></A><H3>
createComplex</H3>
<PRE>
protected <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>createComplex</B>(double&nbsp;realPart,
                                double&nbsp;imaginaryPart)</PRE>
<DL>
<DD>Create a complex number given the real and imaginary parts.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>realPart</CODE> - Real part.<DD><CODE>imaginaryPart</CODE> - Imaginary part.
<DT><B>Returns:</B><DD>a new complex number instance.<DT><B>Since:</B></DT>
  <DD>1.2</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#valueOf(double, double)"><CODE>valueOf(double, double)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="valueOf(double, double)"><!-- --></A><H3>
valueOf</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>valueOf</B>(double&nbsp;realPart,
                              double&nbsp;imaginaryPart)</PRE>
<DL>
<DD>Create a complex number given the real and imaginary parts.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>realPart</CODE> - Real part.<DD><CODE>imaginaryPart</CODE> - Imaginary part.
<DT><B>Returns:</B><DD>a Complex instance.</DL>
</DD>
</DL>
<HR>

<A NAME="valueOf(double)"><!-- --></A><H3>
valueOf</H3>
<PRE>
public static <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A> <B>valueOf</B>(double&nbsp;realPart)</PRE>
<DL>
<DD>Create a complex number given only the real part.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>realPart</CODE> - Real part.
<DT><B>Returns:</B><DD>a Complex instance.</DL>
</DD>
</DL>
<HR>

<A NAME="readResolve()"><!-- --></A><H3>
readResolve</H3>
<PRE>
protected final <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A> <B>readResolve</B>()</PRE>
<DL>
<DD>Resolve the transient fields in a deserialized Complex Object.
 Subclasses will need to override <A HREF="../../../../../org/apache/commons/math3/complex/Complex.html#createComplex(double, double)"><CODE>createComplex(double, double)</CODE></A> to
 deserialize properly.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>A Complex instance with all fields resolved.<DT><B>Since:</B></DT>
  <DD>2.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getField()"><!-- --></A><H3>
getField</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/complex/ComplexField.html" title="class in org.apache.commons.math3.complex">ComplexField</A> <B>getField</B>()</PRE>
<DL>
<DD>Get the <A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3"><CODE>Field</CODE></A> to which the instance belongs.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html#getField()">getField</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;<A HREF="../../../../../org/apache/commons/math3/complex/Complex.html" title="class in org.apache.commons.math3.complex">Complex</A>&gt;</CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD><A HREF="../../../../../org/apache/commons/math3/Field.html" title="interface in org.apache.commons.math3"><CODE>Field</CODE></A> to which the instance belongs</DL>
</DD>
</DL>
<HR>

<A NAME="toString()"><!-- --></A><H3>
toString</H3>
<PRE>
public <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</A> <B>toString</B>()</PRE>
<DL>
<DD>
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<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A></CODE> in class <CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></CODE></DL>
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